Question

The greatest value of sin x cos x

Answer 1

The maximum value of sinxcosx=1/2

To get this

Multiply with 2 in both numerator and denominator and you will get 2sinxcosx/2

But 2sinxcosx=sin2x

The max value of sin2x is 1 But we have sin2x/2

Therefore,the maximum value is 1/2

Answer 2

Answer:

But we know sin2x=2sin x cos x ⇒ f’(x)=cos2x…

…(i) Putting f’(x)=0,

we get critical points as cos2x=0

Now we will find out the second derivative by deriving equation (i),

we get

⇒ f’’ (x)=-sin 2x.2

⇒ f’’(x)=-2sin2x

Now we will find the value of f’’(x) at x = π/4,

we get Therefore at x = π/4,

f(x) is maximum and π/4 is the point of maxima.

Now we will find the maximum value of sin x cos x by substituting x = π/4, in f(x),

we get f(x)= sin x cos x

Hence the maximum value of sin x cos x is 1/2